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Adapted from Pearson Education, Inc.
Welcome to MM150!Kirsten MeymarisThursday, Dec 9th
Plan for the hour MML Challenge!! Basic Terms in Metric System (5.1) Length, Area, Volume (5.2) Mass and Temperature (5.3) Conversions To and From Metric System (5.4)
Adapted from Pearson Education, Inc.
MML Challenge!!Everyone score 60/60 this week, Unit 5?!
Challenge: Can everyone get 60/60 on your MML Graded Practice this week?! REMEMBER:
1- You can go in and out of the MML all Unit long (through next Tuesday at midnight) 2 - You can keep trying similar problems until you get that one right3 – You can view an example of this problem being worked out4 - You can step through this problem getting feedback at each step5 – You can send me an email with your questions about this problem.
Adapted from Pearson Education, Inc.
5.1
Basic Terms and Conversions within the Metric System
Adapted from Pearson Education, Inc.
Basic TermsCommon Use US Customary Metric System
Length inchfoot, yardmile
centimetermeterkilometer
Area inch2
feet2,yard2
acre
cm2
meter2
hectare
Volume (solid) inch3
foot3 yard3
cm3
meters3
Volume (non-solid, liquid)
ounce, cupquartgallon
milliliter, ccliter
Weight/Mass* ouncepound (lb)ton
gramkilogramtonne
Temperature Fahrenheit Celsius* Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.
Adapted from Pearson Education, Inc.
Metric Prefixestera giga mega kilo hecto deka * deci centi mili micro nano pico
1012 109 106 103 102 101 1 10-1 10-2 10-3 10-6 10-9 10-12
Count how many prefixes/decimal places to move
Put in decimal point (if not already there) Move decimal point to the left/right (adding zeros
where necessary) Smaller to larger? (Left = L ~ Larger) Larger to smaller? (Right = R ~ Smaller)
Adapted from Pearson Education, Inc.
Example: Changing Units within Metric System Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MB
Adapted from Pearson Education, Inc.
Metric Prefixes BA
SE
Adapted from Pearson Education, Inc.
Example: Changing Units within Metric System Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MBSolutions: 54.6 m = 0.0546 km. 0.89 kg = 89,000 cg 1.5 TB = 1,500,000 MB
Adapted from Pearson Education, Inc.
5.2
Length, Area, and Volume
Adapted from Pearson Education, Inc.
Common Use US Customary Metric System
Length inchfoot, yardmile
centimetermeterkilometer
Area inch2
feet2,yard2
acre
cm2
meter2
hectare
Volume (solid) inch3
foot3 yard3
cm3
meters3
Volume (non-solid, liquid)
ounce, cupquartgallon
milliliter, ccliter
Weight/Mass* ouncepound (lb)ton
gramkilogramtonne
Temperature Fahrenheit Celsius* Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.
Adapted from Pearson Education, Inc.
Length
The meter is used to measure things that we normally measure in yards and feet.
Areas are always expressed in square units.
Common Formulas:
2rA
wlA
circle
Area
Adapted from Pearson Education, Inc.
Area Example
The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park.
Adapted from Pearson Education, Inc.
Area Example
The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park.
A = 82.5 25.4
A = 2095.5 m2
Solution: Area = length width.
Adapted from Pearson Education, Inc.
Volume in the Metric System
1 m3 = 1 kL
1 dm3 = 1 L
1 cm3 = 1 mL
Volume in LitersVolume in Cubic Units
cc = cubic centimeters = 1cm3
Common Formulas:
hrv
rV
hwlv
cylinder
sphere
2
3
34
Adapted from Pearson Education, Inc.
Example: Volume Application
A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters?
Adapted from Pearson Education, Inc.
Example: Volume Application
A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters?
Solution:
V r 2h
V 3.14 3 2 12
V 339.12 cm3
V 339.12 mL
Adapted from Pearson Education, Inc.
5.3
Mass and Temperature
Adapted from Pearson Education, Inc.
Common Use US Customary Metric System
Length inchfoot, yardmile
centimetermeterkilometer
Area inch2
feet2,yard2
acre
cm2
meter2
hectare
Volume (solid) inch3
foot3 yard3
cm3
meters3
Volume (non-solid, liquid)
ounce, cupquartgallon
milliliter, ccliter
Weight/Mass* ouncepound (lb)ton
gramkilogramtonne
Temperature Fahrenheit Celsius* Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.
Adapted from Pearson Education, Inc.
Mass
Although weight and mass are not the same, on Earth they are proportional to each other. Mass is a measure of the amount of matter in
an object. Weight is the measure of gravitational pull on
an object.
Adapted from Pearson Education, Inc.
Mass
Weight Mass
Earth
Moon
Adapted from Pearson Education, Inc.
Volume and Mass of Water
Volume in Cubic Units
1 m3 = 1 kL = 1 t (1000 kg)
1 dm3 = 1 L = 1 kg
1 cm3 = 1 mL = 1 g
Mass of WaterVolume in Liters
Adapted from Pearson Education, Inc.
Example: Capacity
A fish tank is 1 m long, 60 cm high and 260 mm wide.
Determine the number of liters that the tank holds.
What is the mass of the water in kilograms.
Adapted from Pearson Education, Inc.
Example: Capacity
A fish tank is 1 m long, 60 cm high and 260 mm wide.
Determine the number of liters that the tank holds.
Adapted from Pearson Education, Inc.
Example: Capacity
A fish tank is 1 m long, 60 cm high and 260 mm wide.
What is the mass of the water in kilograms.
Adapted from Pearson Education, Inc.
Example: Capacity continued
Solution:
Since 1 m3 of water = 1 kL of water, 0.156 m3 = 0.156 kL, or 156 liters of water
Since 1L = 1 kg, 156 L = 156 kg of water.
V l w h
10.26 0.6
0.156 m3
Adapted from Pearson Education, Inc.
Temperature
Water boils212ºF100ºC
Body temperature98.6ºF37ºC
Comfortable room71.6ºF22ºC
Water freezes32ºF0ºC
DescriptionºFºC
Temperature
Adapted from Pearson Education, Inc.
Example: Choose ºF or ºC
The temperature of a can of frozen juice about 2 __.
The temperature of a person with a fever is about 101.5 __.
The temperature of a bowl of hot soup is about 175 __.
Adapted from Pearson Education, Inc.
Example: Choose ºF or ºC
The temperature of a can of frozen juice about 2 __.
The temperature of a person with a fever is about 101.5 __.
The temperature of a bowl of hot soup is about 175 __.
Solution: a) ºC b) ºF c) ºF
Adapted from Pearson Education, Inc.
Conversions
F
9
5C 32
C
5
9F 32
Adapted from Pearson Education, Inc.
Example: Conversions The air temperature on a warm summer
day is about 85ºF. What is the equivalent temperature on the Celsius thermometer?
C
5
9F 32
Adapted from Pearson Education, Inc.
Example: Conversions
The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer? Solution:
C 5
9F 32
C 5
985 32
C 5
953
C 29.4
The equivalent temperature is about 29.4ºC.
Adapted from Pearson Education, Inc.
Example: Conversions
The temperature of a cold glass of milk is about 5ºC . What is the equivalent temperature on the Fahrenheit thermometer?
F
9
5C 32
Adapted from Pearson Education, Inc.
Example: Conversions
The temperature of a cold glass of milk is about 5ºC . What is the equivalent temperature on the Fahrenheit thermometer?
Solution:
The equivalent temperature is about 41ºF.
F 9
5C 32
F 9
55 32
F 9 32
F 41
Adapted from Pearson Education, Inc.
5.4
Dimensional Analysis and Conversions to and from the
Metric System
Adapted from Pearson Education, Inc.
Dimensional Analysis
Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement.
A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1.
Adapted from Pearson Education, Inc.
U.S. Customary Units
1 pint = 2 cups 1 year = 365 days
1 cup (liquid) = 8 fluid ounces
1 day = 24 hours1 ton = 2000 pounds
1 hour = 60 minutes1 pound = 16 ounces
1 minute = 60 seconds1 mile = 5280 feet
1 gallon = 4 quarts1 yard = 3 feet
1 quart = 2 pints1 foot = 12 inches
U.S. Customary Units
Adapted from Pearson Education, Inc.
Dimensional Analysis
Examples of unit fractions:
16 oz
1 lb
1 hr
60 min
12 in.
1 ft
Adapted from Pearson Education, Inc.
Conversion to and from the Metric System - Length
LENGTH
U.S. to Metric
1 inch (in.) ≈ 2.54 centimeters (cm)
1 foot (ft) ≈ 30 centimeters (cm)
1 yard (yd) ≈ 0.9 meter (m)
1 mile (mi) ≈ 1.6 kilometers (km)
Adapted from Pearson Education, Inc.
Conversion to and from the Metric System - Area
AREA
U.S. to Metric
1 square inch (in.2) ≈ 6.5 square centimeters (cm2)
1 square foot (ft2) ≈ 0.09 square meter (m2)
1 square yard (yd2) ≈ 0.8 square meter (m2)
1 square mile (mi2) ≈ 2.6 square kilometers (km2)
1 acre ≈ 0.4 hectare (ha)
Adapted from Pearson Education, Inc.
Conversion to and from the Metric System - Volume
VOLUME
U.S. to Metric
1 teaspoon (tsp) ≈ 5 milliliters (ml)
1 fluid ounce (fl oz) ≈ 30 milliliters (ml)
1 quart (qt) ≈ 0.95 liter (l)
1 gallon (gal) ≈ 3.8 liters (l)
1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)
Adapted from Pearson Education, Inc.
Conversion to and from the Metric System - Weight (Mass)
WEIGHT OR MASS
U.S. to Metric
1 ounce (oz) ≈ 28 grams (g)
1 pound (lb) ≈ 0.45 kilogram (kg)
1 ton (T) ≈ 0.9 tonne (t)
Adapted from Pearson Education, Inc.
Example: Volume and Area
A gas tank holds 22.6 gallons of gas. How many liters is this?
The area of a box is 14.25 in2. What is its area in square centimeters?
Adapted from Pearson Education, Inc.
Example: Volume and Area
A gas tank holds 22.6 gallons of gas. How many liters is this?
Solution:
The area of a box is 14.25 in2. What is its area in square centimeters?
Solution:
3.8 l
22.6 gal = 85.88 lgal
14.25 in2 6.5 cm2
1 in2
92.625 cm2
Adapted from Pearson Education, Inc.
Example: Converting Speed
A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour.
Adapted from Pearson Education, Inc.
Example: Converting Speed
A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour.
Solution:
Since 62 km equals 38.75 mi, 62 kph is equivalent to 38.75 mph.
62 km
1 mi
1.6 km
62
1.6mi 38.75 mi
Adapted from Pearson Education, Inc.
Example: Weight (Mass) Conversion for Medication
A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?
Adapted from Pearson Education, Inc.
Example: Weight (Mass) Conversion for Medication
A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?
Solution:
The dosage of the medication is 73.92 mg.
8 lbs 16 oz
1 lb
4 oz 128 oz 4 oz 132 oz
132 oz28 g
oz
1 kg
1000 g
20 mg
1 kg
73.92 mg